Return to Table of Contents

Size: px
Start display at page:

Download "Return to Table of Contents"

Transcription

1 Return to Table of Contents HAPTER8 C. Electric Potential An ECG records the voltage between points on a subject s skin generated by electrical processes in the heart. This ECG, made while the subject was running on a treadmill, provides information about the heart s performance under stress. Both nature and technology utilize electric energy. A lightning stroke unleashes an enormous amount of electrical potential energy, converting it to heat and light. On a much smaller scale, pulses of electric energy within the human nervous system regulate body functions. Power plants generate electrical energy, which is then distributed through vast electrical networks and used for a variety of purposes (Fig. 8 ). An electrical outlet in your home is part of such a network and provides you with electrical potential energy, which you can use to operate electric lights, appliances, and home electronics. In this chapter we shall begin to use energy concepts in our study of electricity. Before reading this chapter, it is a good idea to review the energy concepts introduced in Chapter 7. Fig. 8 Electrical energy for the lights of Las Vegas is generated many kilometers away at Hoover Dam. The electrical energy comes from the gravitational potential energy of the water stored by the dam. 457

2 458 CHAPTER 8 Electric Potential 8 Electrical Potential Energy and Electric Potential In Chapter 7 we found that the work done by certain forces is independent of path and can be expressed as a decrease in some kind of potential energy. Such forces are called conservative forces. In particular we found that the gravitational force is conservative. When only conservative forces do work on a body, the sum of the body s kinetic energy and potential energy is conserved. For example, a book of mass.0 kg held.0 m above the floor has a gravitational potential energy U G mgy (.0 kg)(9.8 m/s 2 )(.0 m) 9.8 J and a kinetic energy K 0. If the book is dropped to the floor, its total mech - anical energy K U G is conserved because only gravity does work on it and the gravitational force is conservative. Just before it hits the floor, the book s potential energy U G 0, but its kinetic energy equals 9.8 J, since the sum K U G is a constant 9.8 J. As noted in the preceding chapter, Coulomb s law has the same mathematical form as the gravitational force law. Thus the Coulomb force, like the gravitational force, must be conservative. And since any electrostatic force can be considered a sum of Coulomb forces, the total electrostatic force is always conservative. This means that any charge in an electrostatic field has electrical potential energy, U E. This electrical potential energy, like mechanical potential energy, can be converted to other forms of energy, for example, heat and light in the case of a lightning stroke. Definition of Electric Potential The concept of electric potential is closely related to the concept of electrical potential energy. We define the electric potential V at a point in space to be the electrical potential energy per unit charge that a test charge q would have if placed at that point: U E V q (8 ) It follows from this definition that the SI unit for electric potential is joules per coulomb, which is defined to be a volt (abbreviated V) in honor of Alessandro Volta, who invented the electric battery in 800: V J/C (8 2) Since electric potential is measured in volts, it is often loosely referred to as voltage. Keep in mind that we use nearly the same symbol for potential, V, and for the unit of potential, the volt, V, except that the symbol for the unit is not italicized. The definition of electric potential as electrical potential energy per unit charge is analogous to the definition of electric field as the force per unit charge on a test charge. Like the electric field, the electric potential is present whether or not there is a test charge present to experience it. The source of the electric potential is the same charge that is the source of the electric field. However, unlike the electric field, the electric potential is a scalar quantity. It is therefore typically easier to work with the electric potential than with the electric field. When the electric potential at a field point is known, we can easily calculate the electrical potential energy of a charge q placed at that point. It follows from the definition V U E /q that the charge q will have an electrical potential energy U E : U E qv (8 3)

3 8 Electrical Potential Energy and Electric Potential 459 EXAMPLE Using a Test Charge to Find the Potential (a) A test charge q 0 6 C is placed at a point P in space where q has electrical potential energy of 0 4 J (Fig. 8 2). What is the value of the electric potential at that point? (b) Suppose that the original test charge is replaced by a second test charge q C at P. Find the electrical potential energy of the new test charge. SOLUTION (a) Applying Eq. 8, we find U E 0 V 4 J q 00 V 0 6 C Remember that P is at an electric potential of 00 V regardless of the presence or absence of the test charge. Later in this sec - tion we shall see how the electric potential at a point can be calculated from a knowledge of either the electric field or the source charge producing the electric field. (b) Since we know that the electric potential at this point is 00 V, we can apply Eq. 8 3 to find the electrical potential energy of the second test charge placed there. U E qv (2 0 5 C)(00 V) J Fig. 8 2 Potential Difference In Chapter 7 we found that the reference level, or zero point, of gravitational potential energy is arbitrary. Consider, for example, the gravitational potential energy of a book of mass.0 kg falling.0 m from a tabletop to the floor. The book s gravitational potential energy U G is mgy (Eq. 7 4). If we set y 0 at the floor, the book has zero potential energy on the floor and potential energy U G (.0 kg)(9.8 m/s 2 ) (.0 m) 9.8 J on the table. If we set y 0 at the table, the book has zero potential energy there and potential energy 9.8 J on the floor at y.0 m. With either choice of zero point, the physically significant fact remains unchanged: the book s potential energy decreases by 9.8 J as it falls from the table to the floor. The reference level for electrical potential energy is also arbitrary. Only differences in electrical potential energy have physical significance. And since electric potential is defined as electrical potential energy per unit charge, it follows that only differences in electric potential (sometimes called the voltage drop ) have physical significance. We can attach a value to the electric potential at a point only after we have defined a reference level. A voltmeter is a device used to measure the difference in electric potential between two points in an electric circuit (Fig. 8 3). Voltmeters will be discussed in Chapter 20. Fig. 8 3 This voltmeter measures a potential difference of V. This book is licensed for single-copy use only. It is prohibited by law to distribute copies of this book in any form.

4 460 CHAPTER 8 Electric Potential EXAMPLE 2 Charge Travelling From One Battery Terminal to Another The terminals of a 2 V battery differ in electric potential by 2 SOLUTION We calculate the loss in potential energy by V, with the positive terminal being at the higher potential, as indicated in Fig Suppose that a 3.0 C charge travels from A to B. How much electrical potential energy does it lose? relating the potential energy to the potential at points A and B, using Eq. 8 3: U E,A U E,B qv A qv B q(v A V B ) (3.0 C)(2 V) 36 J Fig. 8 4 Notice that we have not assigned values to the potential at A and B. The result is independent of these values, so long as V A is 2 V higher than V B. For example, we could have V B 0, V A 2 V, or V B 00 V, V A 2 V, or V B 2 V, V A 0. (a) Uniform Electric Field (b) Uniform Gravitational Field Fig. 8 5 We can find (a) the work done by a uniform electric field on a charge q by considering (b) the work done by gravity on a mass m. Potential Difference in a Uniform Electric Field Calculating electric potential is easiest when the electric field is uniform (Fig. 8 5a). Imagine a positive test charge q traveling from a to b in a uniform field E and subject to a constant force F qe. By applying the definition of work, it is possible to show that the work done by the electric field on q can be expressed as a decrease in the electrical potential energy of q. However, we shall not use this direct but somewhat tedious approach. Instead we shall obtain an expression for electrical potential energy by noting how this situation is mathematically identical to a mass m moving in a uniform gravitational field (Fig. 8 5b). The charge q corresponds to the mass m, and the constant electric field E corresponds to the constant gravitational field g. We solved the gravitational problem in Chapter 7, showing that the work W G done by gravity is independent of path and can be expressed as the decrease in gravitational potential energy from a to b: or W G U G,a U G,b mgy a mgy b mg(y a y b ) U G,a U G,b mgd where d y a y b. Substituting q for m and E for g, we obtain the corresponding expression for the decrease in the electrical potential energy U E of charge q moving from a to b: U E,a U E,b qed Applying the definition of electric potential as electrical potential energy per unit charge, we divide the equation above by q to obtain an expression for the drop in electric potential from a to b: V a V b Ed (in a uniform field) (8 4) We can also obtain this result directly by calculating the work W E the electric field does on q along a particular path from a to b. Let the charge move from a to b by first moving parallel to the field from a to point c (shown in Fig. 8 5a) and then moving perpendicular to the field from c to b. Work is done on q only for the part of the path from a to c. Since there is a constant component of force along this path, the work is the product of this component (F s qe) and the path length d:

5 8 Electrical Potential Energy and Electric Potential 46 W E,a b W E,a c F s s qed The work equals the decrease in the charge s electrical potential energy from a to b. If we divide by q, we again find that the drop in electric potential from a to b is Ed, as we found in Eq. 8 4 for an arbitrary path connecting a and b. The difference in electric potential at two points in an electrostatic field is not always as simply expressed as in Eq. 8 4, which is valid only for a uniform field. However, it is always true that the difference in electric potential depends only on the two points and is the same no matter which path connects the points. We have drawn the electric field in Fig. 8 5a directed vertically downward to emphasize the correspondence with the gravitational field. However, our expression for the drop in electric potential (Eq. 8 4) is applicable to a uniform electric field in any direction, as long as the distance d is measured parallel to field lines and as long as the higher-potential point is upstream in the field from the lower-potential point.* *The term upstream comes from visualizing the electric field as a flowing river, with the direction of the water current in the direction of the electric field. EXAMPLE 3 Finding the Potential Difference Between Two Points in a Uniform Field A uniform electric field of magnitude 2000 N/C is directed SOLUTION (a) Point P is upstream and is therefore at the 37.0 below the horizontal (Fig. 8 6). (a) Find the potential difference between P and R. (b) If we define the reference level of potential so that the potential at R is 500 V, what is the potential at P? higher potential. We apply Eq. 8 4 to compute the drop in potential from P to R. V P V R Ed We must be careful not to identify d as the distance between P and R. Rather, d is the distance along the direction of E and is equal to (5.00 cm)(cos 37.0 ) 4.00 cm. Substituting into the equation above, we find V P V R (2000 N/C)( m) 80.0 V Fig. 8 6 (b) If the potential at R is 500 V, then solving the equation above for V P, we find V P V R 80 V 500 V 80 V 580 V

6 462 CHAPTER 8 Electric Potential EXAMPLE 4 Potential at Points in the Earth s Atmosphere Electric charge on the earth's surface and in the earth s atmosphere produces an electric field that, on a clear day (no thunderstorms), is directed vertically downward and has an approximately constant magnitude of about 00 N/C just above the earth s surface (Fig. 8 7). (a) Find the value of the potential V at an elevation of 0 m and at an elevation of 20 m. Set the potential of the ground equal to zero. (b) If a small positive ion of negligible weight is initially at rest in the atmosphere, which way will the earth s electric field cause it to move, up or down? Which way will the field cause a small negative ion initially at rest to move, up or down? SOLUTION (a) We apply Eq. 8 4 for the potential difference between a point G on the ground and a point P at an elevation of 0 m, setting the ground potential equal to zero: V P V G Ed V P 0 (00 N/C)(0 m) V P 000 V We calculate the potential at a point R at an elevation of 20 m in the same way: V R V G Ed V R 0 (00 N/C)(20 m) V R 2000 V The potential is the same anywhere on a horizontal surface. Any point G on the ground is at a potential of 0, any point P at an elevation of 0 m is at a potential of 000 V, and any point R at an elevation of 20 m is at a potential of 2000 V. (b) As indicated in Fig. 8 8, a positive ion experiences downward force in the direction of the electric field and, in the absence of other forces, will be accelerated downward. A negative ion exper iences an upward force, opposite the electric field, and, in the absence of other forces, will be accelerated upward.* A pos i- tive charge tends to move from higher to lower potential; a negative charge tends to move from lower to higher potential. Fig. 8 7 Fig. 8 8 *There are thousands of positive and negative ions in a cubic centimeter of air on a clear day. The ions move in response to the earth s electric field. These ions are continuously produced by sources of radioactivity on the earth s surface and by cosmic rays entering the earth s atmosphere. The steady flow of positive charges downward and negative charges upward would soon eliminate the negative charge on the earth s surface, were it not for the periodic transfer of negative charges to the ground in lightning strokes. (There are always electrical storms somewhere on earth. See Chapter 9, Problem 33, for calculation of the average number of lightning strokes worldwide at any instant and of your chance of being struck by one.) Since we often encounter situations in which electrons, protons, or other small charges are placed in an electric field, it is convenient to define a new unit of energy that is related to e, the magnitude of the electron or proton charge. This unit, called the electron volt, abbreviated ev, is defined as the electrical potential energy of a charge e at a point where the potential is V. In terms of joules, we express this as or ev ( C)( J/C) ev J (8 5)

7 8 Electrical Potential Energy and Electric Potential 463 EXAMPLE 5 An Ion Accelerated in the Atmosphere Suppose a small positive ion of negligible weight and with a charge q0e is initially at rest in the earth s atmosphere at an elevation of 0 m on a clear day. Use the results of the last example to find the ion s kinetic energy when it hits the ground, assuming (unrealistically) that the ion does not collide with other particles in the atmosphere. SOLUTION In Example 4 we found that the potential at an elevation of 0 m is 000 V and the potential at ground level is zero. Thus the ion moves from a point at a potential of 000 V to a point at zero potential. We are given that the ion s weight is negligible; that is, the gravitational force on the ion is negligible compared with the electric force. So the ion s gravitational potential energy is negligible compared with its electrical potential energy. If we assume that the only significant force acting on the ion is the electric force, the ion s total mechanical energy is con served; that is, the sum of its kinetic energy and electrical potential energy is constant: E f E i K f U E,f K i U E,i Setting the initial kinetic energy equal to zero and applying Eq. 8 3 to relate the ion s electrical potential energy to the potential, we find K f qv f 0 qv i K f q(v i V f ) (0e)(000 V 0) 0,000 ev or, converting to joules,.6 0 K f ( ev) 9 J J ev EXAMPLE 6 Acceleration of Electrons in an Electron Microscope In an electron microscope electrons are accelerated across a high voltage to give a high-energy electron beam that is then scattered off the object being examined. Magnetic fields focus the scattered electrons, forming a highly magnified image on a fluorescent screen. Fig. 8 9a shows an electron microscope and the image it produced of individual uranium atoms. The electron beam is accelerated across a potential difference of 00,000 V (Fig. 8 9b). Each electron starts from rest at a potential of 0 and moves to a point where the potential is V. Find the change (a) in an electron s electrical potential energy and (b) in its kinetic energy. SOLUTION (a) It follows from Eq. 8 3 (U E qv) that U E qv (e)( V 0) ev Notice that the electron, a negative charge, moves from lower to higher potential. This movement corresponds to a loss of potential energy. (b) The electron s weight is a negligible force compared with the electric force. Thus only the electric force does significant work on the electron, and therefore the electron s total mechanical energy is conserved; that is, the sum of the electron s kinetic energy and electrical potential energy is constant. The loss of ev in potential energy must be compensated by a gain of ev in kinetic energy: (a) Fig. 8 9 (b) K U E ( ev) ev

8 464 CHAPTER 8 Electric Potential Fig. 8 0 The electric field does no work on a charge q that moves along a path perpendicular to the field, and so the charge s potential energy is constant. Equipotential Surfaces Suppose a test charge q moves through an electric field in such a way that the path of the charge is always perpendicular to the field (Fig. 8 0). Then the electric force has no component along the path (F s 0), and it follows from the definition of work [Eq. 7 : W (F s s)] that the electric force does no work on the test charge. Because no work is done on q, there is no change in the electrical potential energy of q. Thus this is a path of constant potential. Any path along a surface perpendicular to the field lines is a path of constant potential (Fig. 8 ). The potential is constant over the entire surface, which is called an equipotential surface. An example of equipotential surfaces was seen in Example 4, where we found that, in the earth s vertical electric field, horizontal surfaces are surfaces of constant potential (Fig. 8 8). Since the electric field at the surface of a conductor is everywhere perpendicular to the surface, the surface of any conductor is an equipotential surface (Fig. 8 2). The following example illustrates how equipotential surfaces can be used to determine the magnitude and direction of an electric field. Fig. 8 A test charge q has the same potential energy everywhere on a surface perpendicular to the field lines. Fig. 8 2 A conductor s surface is an equipotential surface because it is perpendicular to the field lines. EXAMPLE 7 Using Equipotential Surfaces to Find an Electric Field Three equipotential surfaces are shown in Fig Draw the corresponding field lines and estimate the field strength at point a, where the distance between the surfaces is 4 cm. SOLUTION The field lines are perpendicular to the equipotential surfaces, as shown in Fig In the vicinity of point a, the surfaces are nearly flat, and so, in order to estimate the field strength, it is a reasonable approximation to use Eq. 8 4 for the potential difference in a uniform field: V a V b Ed V a V b 8 V 6 V E d m 50 V/m Fig. 8 3 Fig. 8 4 The strength of the electric field is often expressed in volts per meter. This is the same unit as newtons per coulomb, as we can see using the definition of a volt: V m J/C JN-m/C m m N C

9 8 Electrical Potential Energy and Electric Potential 465 Potential of a Single Point Charge Next we obtain an expression for potential in the field of a point charge q. Since the electric field produced by q is directed radially, the equipotential surfaces are spherical, as illustrated in Fig. 8 5 for a positive charge q. We could find an expression for the difference in potential energy of a test charge q moving between arbitrary points a and b by computing the work the electric field does on q. Since this calculation requires the use of integral calculus, however, we shall simply state the result without proof. The potential energy of the test charge q at a distance r from the source charge q is kqq U E (8 6) r Applying the definition of the electric potential (V U E q), we obtain an expression for the potential at a distance r from a point charge q: kq V (single point charge) (8 7) r This equation applies to both positive and negative charges. Remember that only potential differences have physical significance, and so when we write an expression for the potential at a point, as we have done here, we are imply - ing that a choice for the reference level of potential has been made. Eq. 8 7 implies that the reference potential is at infinity; that is, when r, the equation gives V 0. Fig. 8 5 Equipotential surfaces of a positive point charge.

10 466 CHAPTER 8 Electric Potential EXAMPLE 8 Equipotential Surfaces for a Point Charge Plot equipotential surfaces and field lines for (a) a point charge q C; (b) a point charge q C. SOLUTION q, we find (a) Applying Eq. 8 7 for any distance r from kq ( V 9 N-m 2 /C 2 )( C) V-m r r r Since V depends only on r, the equipotential surfaces are spheres. Equipotential surfaces are usually drawn so that adjacent surfaces represent equal voltage intervals. Using 3 V intervals, we find that at r.0 m, V 9.0 V at r.5 m, V 6.0 V at r 3.0 m, V 3.0 V at r, V 0 The first three equipotential surfaces in this list are shown in Fig. 8 6a. The fourth surface corresponds to V 0 and is at infinity. (b) For a negative point charge of the same magnitude, only the sign of the potential changes. The equipotential surfaces for this case are shown in Fig. 8 6b. Notice that for both the positive and negative charges the field lines are perpendicular to the equipotential surfaces and are directed from regions of higher potential to regions of lower potential. (a) (b) Fig. 8 6 Cross-sectional views of equipotential surfaces for (a) a positive point charge and (b) a negative point charge. The relationship between the earth s gravitational field and the gravitational potential energy of a kg mass in the field is similar to the relationship between V and E for a negative point charge (Fig. 8 7). Gravitational potential energy is constant along spherical surfaces, which are perpendicular to the gravitational field g. The field lines are directed from surfaces of higher gravitational potential energy to surfaces of lower gravitational potential energy. Fig. 8 7 Spherical surfaces of constant gravitational potential energy. Potential of Several Point Charges Suppose that the electric field in a certain region of space is produced by a collection of n point charges q, q 2,, q n. Each charge q i produces a field E i, and the total field E is the vector sum of the single-particle fields. The work E does on a test charge q is therefore the sum of the work done by the single-particle fields. The electrical potential energy of q at any point is a sum of potential energy terms, each of which corresponds to one of the charges q, q 2,, q n. And the potential (the electrical potential energy per unit charge) is the sum of the single-particle potentials: kq kq 2 V kq n r r2 rn

11 8 Electrical Potential Energy and Electric Potential 467 We can factor k from this equation and express the result more concisely using sum - mation notation: q V k (point charges) (8 8) r As illustrated in Fig. 8 8, the field point P at which V is to be evaluated is at a dis - tance r from source charge q, a distance r 2 from source charge q 2, and so on. Unlike the calculation of the electric field, the calculation of V involves a simple scalar sum. One of the simplest charge configurations is a set of two point charges of equal magnitude but opposite sign separated by some distance. Two such charges are said to form an electric dipole. Equipotential surfaces and field lines are sketched for an electric dipole in Fig Fig. 8 8 The field point where V is to be evaluated is at various distances r, r 2,, r n from the charges q, q 2,, q n that are the source of V. Fig. 8 9 Equipotential surfaces and field lines of an electric dipole. EXAMPLE 9 Dipole Potential An electric dipole consists of charges q (20/9.0) 0 9 C and q 2 (20/9.0) 0 9 C separated by a distance of 6.0 m. Find the potential produced by the dipole for the following field points, all of which are on the line joining the two charges: (a) r.0 m, r m; (b) r 2.0 m, r m; (c) r 3.0 m, r m; (d) r 4.0 m, r m; (e) r 5.0 m, r 2.0 m. A proton is released from rest at point a; find its speed when it reaches point d. SOLUTION Applying Eq. 8 8 for arbitrary values of r and r 2, we find q V k r C 0 9 C ( N-m 2 /C 2 ) r (20 V-m) r r2 Evaluating this expression at field points a to e, we find.0 m 2.0 m 3.0 m 4.0 m 5.0 m 5.0 m 4.0 m 3.0 m 2.0 m.0 m V a (20 V-m) V b (20 V-m) 6 V 5.0 V V c (20 V-m) 0 V V d (20 V-m) 5.0 V V e (20 V-m) 6 V r 2 The values of V at the respective field points are indicated in Fig A proton released from rest at point a will be accelerated to the right in the direction of the electric field. It will go from a higher potential to a lower potential. Its change in potential energy from a to d is found when Eq. 8 3 (U E qv) is applied: U E qv (e)(v d V a ) e(5.0 V 6 V) 2 ev Since the proton s total mechanical energy must be conserved, its kinetic energy must increase by 2 ev: K K f K i 2 ev And since the proton was initially at rest, K i 0. Thus or K f 2 ev K f (2 ev)( J/eV) J Using the definition of kinetic energy and the proton s mass, we find 2 K f mv f 2 v f 2K 2( f J) m kg m/s Fig. 8 20

12 468 CHAPTER 8 Electric Potential EXAMPLE 0 Potential Near Three Point Charges Point charges are located at three corners of a square (Fig. 8 2). (a) Find the potential at P and R. (b) An electron initially at rest at R moves to P and is acted upon only by the electrostatic force. Find the speed of the electron at P. SOLUTION (a) At P, we find V P k q r ( N-m 2 /C 2 ) 52.7 V At R we find C 0.00 m C m (b) The potential energy of the electron at a point where the potential is V is U E qv ev. Thus the change in the electron s potential energy is U E ev C m C 0.00 m.00 0 V R ( N-m 2 /C 2 ) 9 C C m m Fig. 8 2 If no other forces act on the electron, its mechanical energy is conserved and hence its change in kinetic energy is K U E ev Expressing kinetic energy in terms of the electron s mass and speed, and using the fact that the electron s initial speed is zero, we find or 2 mv 2 K ev 2eV v 2( C)(52.7 V 0) m kg m/s Fig A capacitor consists of two conductors carrying opposite charges of equal magnitude. 8 2 Capacitance A capacitor is a simple device for storing charge. It consists of two conductors separated by a small space. Each conductor carries a net charge. The charges are equal in magnitude but opposite in sign (Fig. 8 22). Thus the net charge on the entire capacitor is zero. Capacitors of all shapes and sizes are important elements in electric circuits (Fig. 8 23a). Some capacitors are used to tune radio circuits; others are used to store energy that can be quickly discharged and used as the source of energy for a laser (Fig. 8 23b). Whatever their purpose, all capacitors have the common function of storing charge. If the charge shown on the conductors in Fig is increased, the electric field will increase, and so the potential difference between the two conductors will also increase. The relationship between the charge Q and the potential difference is particularly simple: These two quantities are directly proportional. To have more concise notation we now adopt the convention of using V to denote a potential difference rather than the potential at a single point: V V a V b (8 9)

13 8 2 Capacitance 469 Using this convention, we can express very concisely the relationship between charge and potential difference: Q V (8 0) This result is proved in general in advanced texts on electricity. We shall verify it shortly in one important special case. The constant of proportionality in the relationship above is called capacitance and is denoted by C: Q CV (8 ) It follows from this equation that capacitance must have units of coulombs per volt. We call this unit a farad (abbreviation F), in honor of Michael Faraday: (a) F C/V (8 2) Capacitance is a measure of how much charge a capacitor can store for a given potential difference V. For example, a 2 F capacitor stores twice as much charge as a F capacitor, if both have the same potential difference between their conductors. Parallel-Plate Capacitor The size and shape of a capacitor determine the value of its capacitance. A common and particularly simple geometry is the parallel-plate capacitor (Fig. 8 24). We assume here that the plates are separated by a vacuum. Since the electric field between the plates is uniform, we may apply Eq. 8 4 and express the potential difference as the product of the field strength E and the plate separation d: V Ed In Chapter 7 we found that the field strength just outside a conductor is a function of the surface charge density (Eq. 7 8): Q E 4k 4k A (b) Fig (a) Capacitors found in electric circuits. (b) Capacitors used to energize a very powerful laser. Inserting this expression for E into the equation above, we obtain Solving for Q, we find V 4k Q d A A Q V 4kd This verifies the linear relationship between Q and V for the parallel-plate geometry (Eq. 8 : Q CV ) and gives an expression for the capacitance, which is just the factor in parentheses in the equation above: C A 4kd The capacitance of any capacitor is a constant the value of which depends on the geometry of the capacitor. For the parallel-plate capacitor, capacitance depends only on the area A of the plates and the distance d between them. One can increase capacitance by either increasing A or decreasing d. It is convenient to define a new quantity 0, which will simplify the preceding equation as well as other equations in later chapters. Defining Fig A parallel-plate capacitor.

14 470 CHAPTER 8 Electric Potential 0 (8 3) 4k we may express the capacitance 0 A C (parallel-plate capacitor) (8 4) d We find the value of 0 by substituting the value of k into Eq. 8 3: C 2 /N-m 4( N-m 2 /C 2 ) The units for 0 can be simplified: C 2 /N-m 2 C/V-m F/m. Thus F/m (8 5) EXAMPLE Plate Area of a F Capacitor Calculate the area of one plate of a parallel-plate capacitor having a capacitance of.00 F if the plates are separated by a distance of.00 mm. Such a capacitor would be enormously large, which means that F is a huge amount of capacitance. Units of microfarads (F) and picofarads (pf) are commonly used, where SOLUTION Solving Eq. 8 4 for A, we find Cd A 0 (.00 F)( m) F/m m 2 F 0 6 F pf 0 2 F Typically we encounter capacitors with capacitance on the order of a few F or less. Fig We can charge a capacitor by connecting its plates to a battery. Charging a Capacitor We can charge a capacitor by connecting its plates to the terminals of a battery or power supply (Fig. 8 25). (A power supply is a device used like a battery but which receives its energy from the electrical outlet it plugs into.) The battery or power supply is a source of electrical energy and produces a fixed potential difference across its terminals. Each terminal is connected to one capacitor plate by a metal wire. The terminal, connecting wire, and capacitor plate form one continuous conductor. And since a conductor is at a constant potential, each capacitor plate is at the same potential as the terminal to which it is connected. So the battery or power supply maintains a fixed potential difference across the capacitor, and this means there must be charge on the capacitor. The plates of a capacitor always have charges of opposite sign and equal magnitude. Whenever a charge is established on one capacitor plate, an opposite charge is quickly drawn toward it from the other plate. The opposing charges are attracted to the inner surfaces of the two plates. When the opposite charges have equal magnitude, the electric fields produced by the two charged surfaces cancel everywhere except between the plates. If the charge magnitudes were unequal, a net electric field would exist inside the metal of the plates. Charge would then flow until the field disappeared, that is, until the opposite charges were equal in magnitude.

15 ^^ 8 2 Capacitance 47 If a potential difference is established across a capacitor and then the energy source is disconnected, the capacitor will continue to store charge on the inner surfaces of its plates. If you then provide a conducting path across the plates, they will quickly discharge through the conducting path. If the stored charge is large enough, the discharge is accompanied by a bright spark and a loud sound like a firecracker (Fig. 8 26). It can be dangerous to handle large capacitors. If your body happens to provide a conducting path through which such a capacitor discharges, the result could be painful or even fatal. Parallel Capacitors In electric circuits we often find a combination, or network, of many capacitors. To simplify the analysis of a circuit, it is convenient to be able to represent the effect of all the capacitors in the network by a single equivalent capacitor that produces the same effect for circuit points outside the network. We shall consider two important ways of combining capacitors: series and parallel combinations. When two or more capacitors are connected in such a way that each must have the same potential difference across its plates, the capacitors are said to be connected in parallel. A parallel combination is accomplished when the plates are connected as shown in Fig All the plates and wires connected to each other must be at the same potential because they are all part of one continuous conductor. Thus in Fig the two plates on the left side are both at the same potential V a, and the two plates on the right side are both at potential V b. The potential difference across the two capacitors must then be the same: V a V b. It is convenient to represent a capacitor by the symbol and to represent ideal conducting wires by straight lines. Then the parallel combination shown in Fig can be represented as shown in Fig (Although the symbol for a capacitor suggests parallel plates, it can represent a capacitor with any kind of geometry.) The total charge Q stored on a parallel combination of capacitors is the sum of the charges on the individual capacitors: Q Q Q 2 where the charge on each capacitor equals the product of its capacitance and the same potential difference V: Q C V C 2 V (C C 2 )V A single capacitor having a capacitance C C C 2 stores the same charge Q when the same potential V is applied across it. Thus C is the equivalent capacitance for this combination: C C C 2 The derivation above is easily generalized to three or more capacitors connected in parallel, with the result that the equivalent capacitance is just the sum of the individual capacitances: Fig A discharging capacitor. Fig Two capacitors connected in parallel. C C C 2 C 3 (capacitors in parallel) (8 6) For example, if 5 F, 0 F, and 20 F capacitors are connected in parallel, this is equivalent to a single 35 F capacitor. Fig Circuit diagram of two capacitors connected in parallel.

16 472 CHAPTER 8 Electric Potential Series Capacitors When two capacitors are connected as in Fig. 8 29, they are said to be in series. With this kind of connection, the same charge Q is stored on each capacitor. We can understand this by realizing that before the capacitors are connected to some power source they are uncharged. When the capacitors are charged, the negative charge on the bottom plate of C must come from electrons drawn from the upper plate of C 2, since these two plates are not connected to anything else. So these two isolated plates must have opposite charges, Q and Q (Fig. 8 29). The total potential difference V between points a and b in Fig must equal the sum of the potential differences V and V 2 across the two capacitors because it is only between the capacitors plates that there is any change in potential (remember that there is no change in potential along the connecting wires): Fig Circuit diagram of two capacitors connected in series. V V V 2 When we express the potential difference across each capacitor in terms of its capacitance, the equation above becomes Q V C2 Q C C2 C We wish to find the equivalent capacitance for this series combination; that is, we want the value of capacitance C for the single equivalent capacitor that will store the same charge Q for the same potential difference V. The potential difference across this single equivalent capacitor may be expressed V Equating the two expressions above for V, we obtain an equation for the equivalent capacitance C: or Q Q C C2 C Q C C2 C The derivation above is easily generalized to three or more capacitors connected in series, with the result that the inverse of the equivalent capacitance is just the sum of the inverses of all the individual capacitances: C C2 C3 (capacitors in series) (8 7) C Thus, for example, if three 5 F capacitors are connected in series, the sum of the 3 inverses is (F) 5, and the equivalent capacitance is 3 5 F. Complex networks of capacitors can often be reduced to a single equivalent capacitor when the rules for series and parallel combinations are applied. Q C This book is licensed for single-copy use only. It is prohibited by law to distribute copies of this book in any form.

17 8 2 Capacitance 473 EXAMPLE 2 Equivalent Capacitance of a Network (a) Find the equivalent capacitance of the network shown in Fig (b) Find the charge stored on the 2 F capacitor when the potential difference between a and b is 00 V. The original network stores the same charge. Since the 2 F capacitor is connected directly to point a, 200 C must be stored on this capacitor. SOLUTION (a) We reduce the network in steps, looking for either series or parallel combinations. The F and 3 F capacitors are in parallel, and the 2 F and 4 F capacitors are in parallel. Thus these combinations can be replaced by 4 F and 6 F equivalent capacitors, as indicated in Fig. 8 3a. Now we have three capacitors in series. Adding inverses, we find the inverse of the equivalent capacitance (Fig. 8 3b). C 4 F 6 F 2 F Fig (F) 2 2 F Thus C 2 F (b) For a 00 V potential difference applied between a and b, the equivalent capacitor stores charge Q CV (2 F)(00 V) 200 C Fig. 8 3 Energy Stored by a Capacitor Since a capacitor maintains charge at a potential difference, it stores electrical potential energy. We can calculate the amount of energy stored by recognizing that the effect of charging a capacitor is to transfer a quantity of charge from one plate to the other (Fig. 8 32). Suppose that the charge is transferred bit by bit. As a small quantity of positive charge q moves from the negative plate to the positive plate, it moves to a point at a higher potential and its electrical potential energy therefore increases. The increase in electrical potential energy equals the product of the charge q and the potential difference between the plates. But the value of the capacitor s potential difference depends on how much charge has already been transferred. Just before the charging begins, this potential difference is zero; at the end of the process, the potential difference has reached a final value V. The average potential during the charging is half this final value: Average potential difference The total potential energy U E stored by the charged capacitor equals the sum of the increases in potential energy of all the charge increments q, that is, the increase in potential energy of all the transferred charge Q. This increase in potential energy equals the product of the charge times the average value of the potential difference: 2 V Fig Transferring charge Q from a capacitor s left plate to its right plate gives the left plate a charge Q and the right plate a charge Q.

18 474 CHAPTER 8 Electric Potential U E Q( V) 2 U E QV (8 8) 2 Since Q CV, we may substitute for either Q or V in Eq. 8 8 and express U E in two alternative forms: U E CV 2 (8 9) 2 Q U E 2 (8 20) 2 C EXAMPLE 3 Energy Stored by Capacitators Before and After Connecting Them A 4.00 F capacitor is initially isolated and has a potential difference of 0.0 V across its plates. The plates of this capacitor are then connected in parallel to the plates of an initially uncharged 2.0 F capacitor. Find the electrical potential energy stored before and after connection. SOLUTION Applying Eq. 8 9, we compute the initial electrical potential energy U E : U E CV 2 2 ( F)(0.0 V) J After the capacitors are connected in parallel, we have an equivalent capacitance of 6.0 F. The total charge stored on the two capacitors equals the charge initially stored on the 4.00 F capacitor: Q CV ( F)(0.0 V) C 40.0 C Applying Eq. 8 20, we compute the final potential energy U E : This energy is considerably less than the J originally stored by the 4.00 F capacitor. Thus most of the initial electrical potential energy has been lost. We can understand this loss by considering what happens when the two capacitors are con - nected. They are connected in parallel and so must have the same potential difference between their plates. Since Q CV, the final charge stored on each capacitor is proportional to its capacitance. Thus the 2.0 F capacitor stores three times as much charge as the 4.00 F capacitor, that is, three fourths of the available 40.0 C. Therefore 30.0 C of charge must flow between each plate of the 4.00 F capacitor and the plate of the 2.0 F capacitor to which it is connected, as indicated in Fig During this flow of charge through the connecting wires, most of the initial electrical potential energy is converted to thermal energy. U E 2 2 Q 2 C ( C) F J Fig In order for the system to go from the initial state to the final state, 30.0 C of charge must flow through the connecting wires.

19 Field Energy At this point, you might ask, Exactly where is the potential energy of a charged capacitor stored? To answer this question, we shall first obtain an expression for the electrical potential energy as a function of the electric field between the capacitor plates for the special case of a parallel-plate capacitor. We shall then think of the energy as being stored in the electric field. Such an interpretation will be essential when we consider time-varying fields in later chapters. According to Eq. 8 9, the potential energy stored in a capacitor may be expressed U E CV 2 Using Eq. 8 4 for the capacitance of a parallel-plate capacitor and Eq. 8 4 for the potential difference in a uniform field, we obtain A d U E (Ed)2 8 2 Capacitance AdE 2 2 The volume of space between the plates of the capacitor is filled with a uniform field E. This volume is the product of the area A of each plate and the plate separation d. Thus the energy per unit volume, called the energy density, which we shall denote by u, is found when the expression above is divided by Ad: u 0 E 2 (8 2) 2 We can think of this energy as being stored in the field between the capacitor plates.

20 476 CHAPTER 8 Electric Potential 8 3 Dielectrics Consider an isolated capacitor having charge Q, potential difference V 0 across its plates, and a vacuum between the plates (Fig. 8 34a). Its capacitance C 0 is then C 0 Q V0 Now suppose that a dielectric material, for example, a layer of Teflon, is inserted between the plates (Fig. 8 34b). If we now measure the potential difference across the plates, we find that V is about half the original value V 0. Since there is no way for Q to change in this experiment, this decrease in V means that the ratio of charge to voltage has approximately doubled; there is a new value of the capacitance C that is about twice the vacuum value C 0 : (a) (b) Fig Inserting Teflon between the plates of a capacitor reduces the potential difference from V 0 to 2 V 0. or Q Q Q C 2 V0 V 2 V 0 C 2C 0 When any dielectric is placed between the plates of an isolated capacitor, there is a reduction in potential from the vacuum value and hence an increase in the capacitance. The size of the increase depends on the kind of dielectric. The ratio C/C 0 is called the dielectric constant of the dielectric placed between the plates and is denoted by the Greek letter (kappa): C (8 22) C0 Teflon has a dielectric constant of about 2. Constants for some other common dielec - trics are given in Table 8. Also given in Table 8 are dielectric strengths, defined as the largest electric fields the dielectrics can withstand before breaking down and becoming conductors. For example, air has a dielectric strength of V/m. When the electric field in air exceeds this value, air molecules become ionized and are accelerated by the field, and so the air becomes conducting. This happens, for example, in an electrical storm or when the electric field around a high-voltage transmission line becomes too great. Table 8 Dielectric Constants and Dielectric Strengths Material Dielectric constant Dielectric strength (V/m) Vacuum Air Teflon Paper Glass (Pyrex) Neoprene rubber Porcelain Water Titanium dioxide (exactly)

21 8 3 Dielectrics 477 If we apply Eq to a parallel-plate capacitor, which we found has a vacuum capacitance 0 A C 0, d we obtain an expression for its capacitance when a dielectric is placed between the plates: C C 0 0 A C (parallel-plate capacitor) (8 23) d Solid dielectrics are used in most capacitors. They offer several advantages over either vacuum or air capacitors: () capacitance is increased because of the factor; (2) the dielectric strength is larger than that of air, and so the plates can be closer (smaller d); since C is inversely proportional to d, capacitance is again increased; and (3) the small separation of the plates is easier to maintain when a solid layer of dielectric is inserted between them. EXAMPLE 4 Capacitor with Titanium Dioxide Between the Plates The plates of a parallel-plate capacitor containing a titanium (b) The maximum voltage is the product of the maximum electric field magnitude E (the dielectric strength of titanium dioxide dielectric have an area of cm 2 and are separated by a distance of 0.0 mm. (a) Find the capacitance. dioxide given in Table 8 ) and the plate separation d. (b) What is the maximum voltage that can be appled to this V Ed (2 0 capacitor? 8 V/m)( m) V SOLUTION (a) Applying Eq and using the dielectric con stant of titanium dioxide given in Table 8 ( 00), we find 0 A (00)(8.850 C 2 F/m)(.00 3 cm 2 )(0 2 m/cm) 2 d.00 4 m F 0.89 F Physical Origin of the Dielectric Constant When a dielectric is placed between the plates of a capacitor, the capacitance increases. We can understand this phenomenon in terms of how a dielectric s molecules respond to an electric field. If the charge distribution in a molecule is not symmetric, so that it has positive and negative sides, or poles, it is called a polar molecule. In the absence of an external electric field, polar molecules are randomly oriented (Fig. 8 35a). When an external field is present, polar molecules tend to align with the field so that the positive poles are more likely to point in the direction of the field (Fig. 8 35b). In nonpolar molecules, the charge distribution inside each molecule is electrically symmetric in the absence of a field. However, nonpolar molecules develop poles or (a) (b) Fig (a) Polar molecules are randomly oriented in the absence of an external field. (b) Polar molecules are partially aligned with an external electric field.

22 478 CHAPTER 8 Electric Potential Fig Nonpolar molecules polarized by an external electric field. a dipole moment as it is called when an electric field is present (Fig. 8 36). The amount of polarization developed by nonpolar molecules, however, is not as great as it is in polar molecules. For both polar and nonpolar dielectrics, the net effect of the field is to give the dielectric positive and negative surface charges, as illustrated in Fig for a nonpolar dielectric. When a dielectric is inserted between the plates of a capacitor, dielectric surface charge partially cancels the charge on the surfaces of the capacitor plates. Thus the field between the plates is reduced (Fig. 8 38), and this reduction in field strength reduces the potential difference. The lower potential difference for the same amount of charge stored on the plates means that there is a larger value of capacitance. The effect is greater for polar molecules than for nonpolar ones. For example, water molecules are polar and water has a high dielectric constant ( 80), whereas the dielectric constant for paper, a nonpolar material, is only 4. The argument used to derive the electrical potential energy of a vacuum-filled capacitor also applies when a dielectric is present, and so in either case we may use Eqs. 8 8 to 8 20: Q U E QV 2 CV C Fig The net effect of a dielectric in a uniform electric field is to produce positive and negative surface charges on opposite sides of the dielectric. Eq. 8 2 for the energy density of the electric field must, however, be modified. That equation was derived from the expression U E CV 2 2, from which we found the energy density u 0 E 2 2. If we substitute C C 0 into the expression for U E, we may repeat the derivation, which is changed only by the factor. Thus the energy density in a dielectric is u 0 E 2 (8 24) 2 This equation does not imply that the energy density is enhanced over the vacuum value by the factor because E is reduced when a dielectric is placed near free charge. Fig Insertion of a dielectric in a capacitor cancels some of the charge on the plates and therefore reduces the electric field and the potential difference between the plates.

23 8 4 The Oscilloscope 479 *8 4 The Oscilloscope In this section we shall study the motion of an electron in a uniform electric field and the application of this motion to the oscilloscope, an instrument used to display and measure electrical signals (Fig. 8 39). The oscilloscope allows us to see the time dependence of a time-varying potential difference, in effect, to graph the potential difference versus time. Fig An oscilloscope. Fig An oscilloscope s cathode ray tube (simplified). The oscilloscope utilizes a cathode ray tube (CRT) (Fig. 8 40), which is a vacuumsealed, glass tube that is also used as the picture tube in a television. When heated, a metal plate called the cathode emits a beam of electrons (originally called cathode rays). Because there is a potential difference between the cathode and the anode, another metal plate that is maintained at a positive potential relative to the cathode, the electrons are accelerated toward the anode and pass through the hole in its center. The electrons then strike a point on the screen, and the fluorescent material on the screen produces a bright spot of light at that point. The location of the spot can be varied by bending the path of the electron beam. This is accomplished with electric fields generated by the horizontal and vertical deflection plates. We shall show how the deflection produced by each set of plates depends on the potential difference applied to them and on the cathode-to-anode potential difference, which accelerates the electrons.

24 480 CHAPTER 8 Electric Potential Fig. 8 4 When the electric field between the vertical deflection plates of a CRT is directed downward, the electron beam is deflected upward. Consider the effect on the electrons of the electric field produced by the vertical deflection plates (Fig. 8 4). Suppose that at some instant there is a potential difference V between the plates, with the upper plate at the higher potential. Then the field is directed downward and has magnitude E V/d where d is the spacing between the plates. Because the electrons have a negative charge, this field produces a constant upward force F qe ee, and hence a constant upward acceleration a y. The electrons enter the electric field with only a horizontal velocity v x. They leave the field having moved upward only slightly, as shown in the figure, but with a newly acquired vertical velocity component v y, given by F y t ee v y a y t m t m where m is the mass of an electron and t is the time during which the electrons are in the field. This time t is related to the length x of the plates and to the horizontal component of velocity v x by the equation x t vx Combining the three preceding equations, we obtain exv v y dmvx The deflection D of the electron beam is determined by the angle at which the beam leaves the field. From the figure we see that tan Inserting the preceding expression for v y, we find D The velocity v x at which the electrons enter the field is determined by the cathode-toanode potential difference that accelerated them as they left the cathode. We denote this potential difference by V and note that the electron s gain in kinetic energy mv x2 equals its loss in potential energy ev, or mv x2 2eV. Using this in the equation 2 above, we obtain D exv dmvx 2 v y vx xv D (8 25) 2dV

25 8 4 The Oscilloscope 48 Thus we see that the deflection is directly proportional to the potential difference V across the deflecting plates and inversely proportional to the potential difference V between anode and cathode. The same equation applies to horizontal deflections produced by applying a potential difference to the horizontal deflection plates. EXAMPLE 5 Electron Beam Deflection When V is Applied to an Oscilloscope s Plates Suppose that an oscilloscope s CRT has the following dimensions: 40 cm, x 5 cm, and d cm. Let the accelerating potential V between cathode and anode be 000 V and the deflection voltage V be V across either set of deflection plates. Find the deflection of the electron beam. The deflection is directly proportional to V. Thus a 0 V potential difference applied to the deflection plates produces a cm deflection, 20 V produces a 2-cm deflection, and so on. The deflection of the electron beam for a given deflection-plate voltage is determined by a setting of the oscilloscope s controls, which determine the cathode-to-anode accelerating voltage. SOLUTION Applying Eq. 8 25, we find This example corresponds to a setting of 0 V/cm. xv (0.4 m)(0.05 m)( V) D 0 3 m 0. cm 2dV 2(0.0 m)(000 V) Eq shows that the deflection D of an oscilloscope s electron beam is proportional to the potential difference V applied across its deflection plates, as illustrated in the preceding example. Thus an oscilloscope can be used to measure the potential difference across its plates. With no voltage applied to either set of plates, a dot of light is seen at the center of the screen (Fig. 8 42a). When the beam is deflected 3 cm vertically (Fig. 8 42b), with the control set at 0 V/cm, we know that there is a potential difference of 30 V across the vertical deflection plates. The oscilloscope is equipped with metal probes that connect the internal deflection plates with points outside in order to measure the potential difference between those points (Fig. 8 43). Since they are connected to the external points by good conductors, the plates are at the same potential as those points. As mentioned in Section 8, voltmeters are used to measure a constant potential difference. The oscilloscope, however, may also be used to observe and measure potential differences that vary with time, especially periodic potential differences. This is one of the most important functions of an oscilloscope, and so we describe it here, although it involves time-varying fields, which we shall not discuss in detail until Chapter 2. The oscilloscope may be set to internal sweep. With this setting a circuit inside the oscilloscope applies a time-varying voltage to the horizontal deflection plates, causing the electron beam to sweep horizontally across the face of the screen at a constant speed from left to right and, when it reaches the right side, to jump back almost instantly to the left and repeat the motion. If the sweep rate is slow, one sees a spot of light moving at constant speed across the screen. The image remains on the screen for a brief time after the electron beam sweeps by, however, and so if the sweep rate is rapid enough, one sees a continuous horizontal line. Fig With the vertical deflection control set at 0 V/cm, this electron beam is (a) undeflected when no voltage is applied; (b) deflected 3 cm when 30 V is applied to the vertical plates. Fig Metal probes connected to an oscilloscope s deflection plates allow one to measure the potential difference between two points.

26 482 CHAPTER 8 Electric Potential (a) (b) Fig Oscilloscope image when (a) a constant voltage is applied to the vertical plates; (b) alternating positive and negative voltages are applied to the vertical plates. Fig The voltage measured by this oscilloscope is a sine function of time. Suppose that, with a fast horizontal sweep, a constant voltage is applied to the vertical plates. Then the beam is deflected as shown in Fig. 8 44a. Next suppose that a time-varying voltage is applied to the vertical plates. Then the time variation will be graphically displayed on the screen. For example, if the voltage alternates between equal positive and negative values, such as 0 V for 0 2 s, then 0 V for 0 2 s, then 0 V again, and if the sweep rate is adjusted so that the beam travels across every s, the display will be as shown in Fig. 8 44b. The constant horizontal velocity of the electron beam makes the horizontal axis effectively a time axis. Adjustable controls on the oscilloscope indicate the number of seconds or milliseconds per cm on the horizontal axis, that is, the time required for the beam to move past one horizontal division. Thus the oscilloscope allows us to obtain detailed information about the voltage applied to its vertical plates and how that voltage varies with time. For example, if the display shown in Fig is seen on the screen of an oscilloscope that has its vertical deflection set at mv/cm and its sweep rate set at 2 ms/cm, we know that the voltage being measured is time-dependent a sine function of time having an amplitude of 3 mv (3 cm mv/cm) and a period of 8 ms (4 cm 2 ms/cm), or a frequency of /(8 0 3 s) 25 Hz. The oscilloscope can be used to analyze any kind of time-dependent phenomenon that can be converted to a time-dependent voltage. For example, a sound produced by the human voice or by a musical instrument can be converted by means of a microphone to a voltage that has the same time dependence as the sound wave and can be displayed on the screen of an oscilloscope (Fig. 8 46a). One can also use the oscilloscope to monitor electrical voltages generated by the human body. For example, electrodes connected from the oscilloscope to points on the head can pick up tiny voltages, on the order of microvolts, produced by processes within the brain. (The signals must be amplified first.) The subject s mental state (alert, relaxed, drowsy) is reflected in the kind of pattern that is observed. The record of potential versus time is called an electroencephalogram, abbreviated EEG (Fig. 8 46b). Similarly, the heart s activity can be monitored by electrodes connected to various parts of the body, and the resulting record of potential versus time is called an electrocardiogram, abbreviated ECG, or EKG. An example of an ECG is shown at the beginning of this chapter. Irregularities in the functioning of the brain or heart are reflected in abnormal EEG s or ECG s respectively. A television picture tube is similar to an oscilloscope tube except that in the television tube the deflection is accomplished by means of magnetic fields (discussed in Chapter 2) rather than electric fields. In this case the electron beam sweeps horizontally first across the top of the screen, varying in intensity according to the image being displayed, sweeps across again but displaced a bit lower on the screen, and repeats this process until the screen is covered with 525 lines in a total time of eye sees a complete image covering the entire screen. 30 of a second. The Fig An oscilloscope can be used to observe (a) sound waves and (b) brain waves. (b)

Chapter 1 The Electric Force

Chapter 1 The Electric Force Chapter 1 The Electric Force 1. Properties of the Electric Charges 1- There are two kinds of the electric charges in the nature, which are positive and negative charges. - The charges of opposite sign

More information

Energy Stored in Capacitors

Energy Stored in Capacitors Energy Stored in Capacitors U = 1 2 qv q = CV U = 1 2 CV 2 q 2 or U = 1 2 C 37 Energy Density in Capacitors (1) We define the, u, as the electric potential energy per unit volume Taking the ideal case

More information

Chapter 17 Electric Potential

Chapter 17 Electric Potential Chapter 17 Electric Potential Units of Chapter 17 Electric Potential Energy and Potential Difference Relation between Electric Potential and Electric Field Equipotential Lines The Electron Volt, a Unit

More information

EL FORCE and EL FIELD HW-PRACTICE 2016

EL FORCE and EL FIELD HW-PRACTICE 2016 1 EL FORCE and EL FIELD HW-PRACTICE 2016 1.A difference between electrical forces and gravitational forces is that electrical forces include a. separation distance. b. repulsive interactions. c. the inverse

More information

iclicker A metal ball of radius R has a charge q. Charge is changed q -> - 2q. How does it s capacitance changed?

iclicker A metal ball of radius R has a charge q. Charge is changed q -> - 2q. How does it s capacitance changed? 1 iclicker A metal ball of radius R has a charge q. Charge is changed q -> - 2q. How does it s capacitance changed? q A: C->2 C0 B: C-> C0 C: C-> C0/2 D: C->- C0 E: C->-2 C0 2 iclicker A metal ball of

More information

Chapter 16. Electric Energy and Capacitance

Chapter 16. Electric Energy and Capacitance Chapter 16 Electric Energy and Capacitance Electric Potential Energy The electrostatic force is a conservative force It is possible to define an electrical potential energy function with this force Work

More information

Chapter 21 Electric Potential

Chapter 21 Electric Potential Chapter 21 Electric Potential Chapter Goal: To calculate and use the electric potential and electric potential energy. Slide 21-1 Chapter 21 Preview Looking Ahead Text: p. 665 Slide 21-2 Review of Potential

More information

19 ELECTRIC POTENTIAL AND ELECTRIC FIELD

19 ELECTRIC POTENTIAL AND ELECTRIC FIELD Chapter 19 Electric Potential and Electric Field 733 19 ELECTRIC POTENTIAL AND ELECTRIC FIELD Figure 19.1 Automated external defibrillator unit (AED) (credit: U.S. Defense Department photo/tech. Sgt. Suzanne

More information

12/15/2015. Newton per Coulomb N/C. vector. A model of the mechanism for electrostatic interactions. The Electric Field

12/15/2015. Newton per Coulomb N/C. vector. A model of the mechanism for electrostatic interactions. The Electric Field Chapter 15 Lecture The Electric Field A model of the mechanism for electrostatic interactions A model for electric interactions, suggested by Michael Faraday, involves some sort of electric disturbance

More information

Nicholas J. Giordano. Chapter 18. Electric Potential. Marilyn Akins, PhD Broome Community College

Nicholas J. Giordano.  Chapter 18. Electric Potential. Marilyn Akins, PhD Broome Community College Nicholas J. Giordano www.cengage.com/physics/giordano Chapter 18 Electric Potential Marilyn Akins, PhD Broome Community College Electric Potential Electric forces can do work on a charged object Electrical

More information

Electric Potential Energy Chapter 16

Electric Potential Energy Chapter 16 Electric Potential Energy Chapter 16 Electric Energy and Capacitance Sections: 1, 2, 4, 6, 7, 8, 9 The electrostatic force is a conservative force It is possible to define an electrical potential energy

More information

PHYSICS - Electrostatics

PHYSICS - Electrostatics PHYSICS - Electrostatics Electrostatics, or electricity at rest, involves electric charges, the forces between them, and their behavior in materials. 22.1 Electrical Forces and Charges The fundamental

More information

Objects usually are charged up through the transfer of electrons from one object to the other.

Objects usually are charged up through the transfer of electrons from one object to the other. 1 Part 1: Electric Force Review of Vectors Review your vectors! You should know how to convert from polar form to component form and vice versa add and subtract vectors multiply vectors by scalars Find

More information

Two point charges, A and B, lie along a line separated by a distance L. The point x is the midpoint of their separation.

Two point charges, A and B, lie along a line separated by a distance L. The point x is the midpoint of their separation. Use the following to answer question 1. Two point charges, A and B, lie along a line separated by a distance L. The point x is the midpoint of their separation. 1. Which combination of charges would yield

More information

33 Electric Fields and Potential. An electric field is a storehouse of energy.

33 Electric Fields and Potential. An electric field is a storehouse of energy. An electric field is a storehouse of energy. The space around a concentration of electric charge is different from how it would be if the charge were not there. If you walk by the charged dome of an electrostatic

More information

Chapter 19 Electric Potential and Electric Field

Chapter 19 Electric Potential and Electric Field Chapter 19 Electric Potential and Electric Field The electrostatic force is a conservative force. Therefore, it is possible to define an electrical potential energy function with this force. Work done

More information

Consider a point P on the line joining the two charges, as shown in the given figure.

Consider a point P on the line joining the two charges, as shown in the given figure. Question 2.1: Two charges 5 10 8 C and 3 10 8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.

More information

General Physics (PHY 2140)

General Physics (PHY 2140) General Physics (PHY 2140) Lecture 5 Electrostatics Electrical energy potential difference and electric potential potential energy of charged conductors Capacitance and capacitors http://www.physics.wayne.edu/~apetrov/phy2140/

More information

PHY101: Major Concepts in Physics I. Photo: J. M. Schwarz

PHY101: Major Concepts in Physics I. Photo: J. M. Schwarz Welcome back to PHY101: Major Concepts in Physics I Photo: J. M. Schwarz Announcements In class today we will finish Chapter 17 on electric potential energy and electric potential and perhaps begin Chapter

More information

Chapter 23 Electric Potential. Copyright 2009 Pearson Education, Inc.

Chapter 23 Electric Potential. Copyright 2009 Pearson Education, Inc. Chapter 23 Electric Potential Units of Chapter 23 Electric Potential Energy and Potential Difference Relation between Electric Potential and Electric Field Electric Potential Due to Point Charges Potential

More information

Lecture PowerPoints. Chapter 17 Physics: Principles with Applications, 6 th edition Giancoli

Lecture PowerPoints. Chapter 17 Physics: Principles with Applications, 6 th edition Giancoli Lecture PowerPoints Chapter 17 Physics: Principles with Applications, 6 th edition Giancoli 2005 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for

More information

Chapter 26. Capacitance and Dielectrics

Chapter 26. Capacitance and Dielectrics Chapter 26 Capacitance and Dielectrics Capacitors Capacitors are devices that store electric charge Examples of where capacitors are used include: radio receivers filters in power supplies to eliminate

More information

Electric Potential. Capacitors (Chapters 28, 29)

Electric Potential. Capacitors (Chapters 28, 29) Electric Potential. Capacitors (Chapters 28, 29) Electric potential energy, U Electric potential energy in a constant field Conservation of energy Electric potential, V Relation to the electric field strength

More information

Matthew W. Milligan. Electric Fields. a figment reality of our imagination

Matthew W. Milligan. Electric Fields. a figment reality of our imagination Matthew W. Milligan Electric Fields a figment reality of our imagination Electrostatics I. Charge and Force - concepts and definition - Coulomb s Law II. Field and Potential - electric field strength &

More information

Chapter 16 Electrical Energy Capacitance. HW: 1, 2, 3, 5, 7, 12, 13, 17, 21, 25, 27 33, 35, 37a, 43, 45, 49, 51

Chapter 16 Electrical Energy Capacitance. HW: 1, 2, 3, 5, 7, 12, 13, 17, 21, 25, 27 33, 35, 37a, 43, 45, 49, 51 Chapter 16 Electrical Energy Capacitance HW: 1, 2, 3, 5, 7, 12, 13, 17, 21, 25, 27 33, 35, 37a, 43, 45, 49, 51 Electrical Potential Reminder from physics 1: Work done by a conservative force, depends only

More information

Chapter Assignment Solutions

Chapter Assignment Solutions Chapter 20-21 Assignment Solutions Table of Contents Page 558 #22, 24, 29, 31, 36, 37, 40, 43-48... 1 Lightning Worksheet (Transparency 20-4)... 4 Page 584 #42-46, 58-61, 66-69, 76-79, 84-86... 5 Chapter

More information

AP Physics Study Guide Chapter 17 Electric Potential and Energy Name. Circle the vector quantities below and underline the scalar quantities below

AP Physics Study Guide Chapter 17 Electric Potential and Energy Name. Circle the vector quantities below and underline the scalar quantities below AP Physics Study Guide Chapter 17 Electric Potential and Energy Name Circle the vector quantities below and underline the scalar quantities below electric potential electric field electric potential energy

More information

Chapter 19 Electric Potential Energy and Electric Potential Sunday, January 31, Key concepts:

Chapter 19 Electric Potential Energy and Electric Potential Sunday, January 31, Key concepts: Chapter 19 Electric Potential Energy and Electric Potential Sunday, January 31, 2010 10:37 PM Key concepts: electric potential electric potential energy the electron-volt (ev), a convenient unit of energy

More information

Exam 1 Solutions. The ratio of forces is 1.0, as can be seen from Coulomb s law or Newton s third law.

Exam 1 Solutions. The ratio of forces is 1.0, as can be seen from Coulomb s law or Newton s third law. Prof. Eugene Dunnam Prof. Paul Avery Feb. 6, 007 Exam 1 Solutions 1. A charge Q 1 and a charge Q = 1000Q 1 are located 5 cm apart. The ratio of the electrostatic force on Q 1 to that on Q is: (1) none

More information

Parallel Plate Capacitor, cont. Parallel Plate Capacitor, final. Capacitance Isolated Sphere. Capacitance Parallel Plates, cont.

Parallel Plate Capacitor, cont. Parallel Plate Capacitor, final. Capacitance Isolated Sphere. Capacitance Parallel Plates, cont. Chapter 6 Capacitance and Dielectrics Capacitors! Capacitors are devices that store electric charge! Examples of where capacitors are used include:! radio receivers (tune frequency)! filters in power supplies!

More information

Chapter 19 Electric Potential and Electric Field Sunday, January 31, Key concepts:

Chapter 19 Electric Potential and Electric Field Sunday, January 31, Key concepts: Chapter 19 Electric Potential and Electric Field Sunday, January 31, 2010 10:37 PM Key concepts: electric potential electric potential energy the electron-volt (ev), a convenient unit of energy when dealing

More information

Copyright by Holt, Rinehart and Winston. All rights reserved.

Copyright by Holt, Rinehart and Winston. All rights reserved. CHAPTER 18 Electrical Energy and Capacitance PHYSICS IN ACTION During a thunderstorm, particles having different charges accumulate in different parts of a cloud. This separation of charges creates an

More information

Electric Potential Practice Problems

Electric Potential Practice Problems Electric Potential Practice Problems AP Physics Name Multiple Choice 1. A negative charge is placed on a conducting sphere. Which statement is true about the charge distribution (A) Concentrated at the

More information

Capacitors (Chapter 26)

Capacitors (Chapter 26) Capacitance, C Simple capacitive circuits Parallel circuits Series circuits Combinations Electric energy Dielectrics Capacitors (Chapter 26) Capacitors What are they? A capacitor is an electric device

More information

Chapter 12 Electrostatic Phenomena

Chapter 12 Electrostatic Phenomena Chapter 12 Electrostatic Phenomena 1. History Electric Charge The ancient Greeks noticed that if you rubbed amber (petrified tree resin) on fur, then the amber would have a property that it could attract

More information

Lecture PowerPoints. Chapter 17 Physics: Principles with Applications, 7 th edition Giancoli

Lecture PowerPoints. Chapter 17 Physics: Principles with Applications, 7 th edition Giancoli Lecture PowerPoints Chapter 17 Physics: Principles with Applications, 7 th edition Giancoli This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching

More information

Objects can be charged by rubbing

Objects can be charged by rubbing Electrostatics Objects can be charged by rubbing Charge comes in two types, positive and negative; like charges repel and opposite charges attract Electric charge is conserved the arithmetic sum of the

More information

Physics (

Physics ( Question 2.12: A charge of 8 mc is located at the origin. Calculate the work done in taking a small charge of 2 10 9 C from a point P (0, 0, 3 cm) to a point Q (0, 4 cm, 0), via a point R (0, 6 cm, 9 cm).

More information

7 ELECTRIC POTENTIAL

7 ELECTRIC POTENTIAL Chapter 7 Electric Potential 285 7 ELECTRIC POTENTIAL Figure 7.1 The energy released in a lightning strike is an excellent illustration of the vast quantities of energy that may be stored and released

More information

UNIT 102-2: ELECTRIC POTENTIAL AND CAPACITANCE Approximate time two 100-minute sessions

UNIT 102-2: ELECTRIC POTENTIAL AND CAPACITANCE Approximate time two 100-minute sessions Name St.No. Date(YY/MM/DD) / / Section UNIT 1022: ELECTRIC POTENTIAL AND CAPACITANCE Approximate time two 100minute sessions I get a real charge out of capacitors. P. W. Laws OBJECTIVES 1. To understand

More information

Chapter 17 & 18. Electric Field and Electric Potential

Chapter 17 & 18. Electric Field and Electric Potential Chapter 17 & 18 Electric Field and Electric Potential Electric Field Maxwell developed an approach to discussing fields An electric field is said to exist in the region of space around a charged object

More information

Chapter 16. Electric Energy and Capacitance

Chapter 16. Electric Energy and Capacitance Chapter 16 Electric Energy and Capacitance Electric Potential of a Point Charge The point of zero electric potential is taken to be at an infinite distance from the charge The potential created by a point

More information

PH 1120 Electricity and Magnetism Term B, 2009 STUDY GUIDE #2

PH 1120 Electricity and Magnetism Term B, 2009 STUDY GUIDE #2 PH 1120 Electricity and Magnetism Term B, 2009 STUDY GUIDE #2 In this part of the course we will study the following topics: Electric potential difference and electric potential for a uniform field Electric

More information

Chapter 10. Electrostatics

Chapter 10. Electrostatics Chapter 10 Electrostatics 3 4 AP Physics Multiple Choice Practice Electrostatics 1. The electron volt is a measure of (A) charge (B) energy (C) impulse (D) momentum (E) velocity. A solid conducting sphere

More information

1. The diagram shows the electric field lines produced by an electrostatic focussing device.

1. The diagram shows the electric field lines produced by an electrostatic focussing device. 1. The diagram shows the electric field lines produced by an electrostatic focussing device. Which one of the following diagrams best shows the corresponding equipotential lines? The electric field lines

More information

End-of-Chapter Exercises

End-of-Chapter Exercises End-of-Chapter Exercises Exercises 1 12 are primarily conceptual questions designed to see whether you understand the main concepts of the chapter. 1. (a) If the electric field at a particular point is

More information

Chapter 26. Capacitance and Dielectrics

Chapter 26. Capacitance and Dielectrics Chapter 26 Capacitance and Dielectrics Circuits and Circuit Elements Electric circuits are the basis for the vast majority of the devices used in society. Circuit elements can be connected with wires to

More information

General Physics (PHY 2140)

General Physics (PHY 2140) General Physics (PHY 2140) Lecture 2 Electrostatics Electric flux and Gauss s law Electrical energy potential difference and electric potential potential energy of charged conductors http://www.physics.wayne.edu/~alan/

More information

Electric Potential Energy Conservative Force

Electric Potential Energy Conservative Force Electric Potential Energy Conservative Force Conservative force or field is a force field in which the total mechanical energy of an isolated system is conserved. Examples, Gravitation, Electrostatic,

More information

Potential from a distribution of charges = 1

Potential from a distribution of charges = 1 Lecture 7 Potential from a distribution of charges V = 1 4 0 X Smooth distribution i q i r i V = 1 4 0 X i q i r i = 1 4 0 Z r dv Calculating the electric potential from a group of point charges is usually

More information

Physics 112 Homework 2 (solutions) (2004 Fall) Solutions to Homework Questions 2

Physics 112 Homework 2 (solutions) (2004 Fall) Solutions to Homework Questions 2 Solutions to Homework Questions 2 Chapt16, Problem-1: A proton moves 2.00 cm parallel to a uniform electric field with E = 200 N/C. (a) How much work is done by the field on the proton? (b) What change

More information

ELECTROSTATIC FIELDS

ELECTROSTATIC FIELDS ELECTROSTATIC FIELDS Electric charge Ordinary matter is made up of atoms which have positively charged nuclei and negatively charged electrons surrounding them. A body can become charged if it loses or

More information

Electric Field of a uniformly Charged Thin Spherical Shell

Electric Field of a uniformly Charged Thin Spherical Shell Electric Field of a uniformly Charged Thin Spherical Shell The calculation of the field outside the shell is identical to that of a point charge. The electric field inside the shell is zero. What are the

More information

Chapter 21 Electrical Properties of Matter

Chapter 21 Electrical Properties of Matter Chapter 21 Electrical Properties of Matter GOALS When you have mastered the contents of this chapter, you will be able to achieve the following goals: Definitions Define each of the following terms, and

More information

Section 16.1 Potential Difference and Electric Potential

Section 16.1 Potential Difference and Electric Potential PROBLEMS 1, 2, 3 = straightforward, intermediate, challenging = full solution available in Student Solutions Manual/Study Guide = biomedical application Section 16.1 Potential Difference and Electric Potential

More information

Electrostatic Potential and Capacitance Examples from NCERT Text Book

Electrostatic Potential and Capacitance Examples from NCERT Text Book Electrostatic Potential and Capacitance Examples from NCERT Text Book 1. (a) Calculate the potential at a point P due to a charge of 4 10 located 9 cm away. (b) Hence obtain the done in bringing a charge

More information

Physics 126 Fall 2004 Practice Exam 1. Answer will be posted about Oct. 5.

Physics 126 Fall 2004 Practice Exam 1. Answer will be posted about Oct. 5. Physics 126 Fall 2004 Practice Exam 1. Answer will be posted about Oct. 5. 1. Which one of the following statements best explains why tiny bits of paper are attracted to a charged rubber rod? A) Paper

More information

Chapter 17. Electric Potential Energy and the Electric Potential

Chapter 17. Electric Potential Energy and the Electric Potential Chapter 17 Electric Potential Energy and the Electric Potential Consider gravity near the surface of the Earth The gravitational field is uniform. This means it always points in the same direction with

More information

Chapter 17 Lecture Notes

Chapter 17 Lecture Notes Chapter 17 Lecture Notes Physics 2424 - Strauss Formulas: qv = U E W = Fd(cosθ) W = - U E V = Ed V = kq/r. Q = CV C = κε 0 A/d κ = E 0 /E E = (1/2)CV 2 Definition of electric potential Definition of Work

More information

Chapter 26. Capacitance and Dielectrics

Chapter 26. Capacitance and Dielectrics Chapter 26 Capacitance and Dielectrics Capacitors Capacitors are devices that store electric charge Examples of where capacitors are used include: radio receivers filters in power supplies to eliminate

More information

P202 Practice Exam 1 Spring 2004 Instructor: Prof. Sinova

P202 Practice Exam 1 Spring 2004 Instructor: Prof. Sinova P202 Practice Exam 1 Spring 2004 Instructor: Prof. Sinova Name: Date: 1. Each of three objects has a net charge. Objects A and B attract one another. Objects B and C also attract one another, but objects

More information

Electric Fields Part 1: Coulomb s Law

Electric Fields Part 1: Coulomb s Law Electric Fields Part 1: Coulomb s Law F F Last modified: 07/02/2018 Contents Links Electric Charge & Coulomb s Law Electric Charge Coulomb s Law Example 1: Coulomb s Law Electric Field Electric Field Vector

More information

Recap: Electric Field Lines Positive Charge: field lines outwards direction Negative Charge: converge F + In both cases density

Recap: Electric Field Lines Positive Charge: field lines outwards direction Negative Charge: converge F + In both cases density Recap: Electric Field Lines Concept of electric field lines initially used by Michael Faraday (19 th century) to aid visualizing electric (and magnetic) forces and their effects. James Clerk Maxwell (19

More information

Polarization. Polarization is not necessarily a charge imbalance!

Polarization. Polarization is not necessarily a charge imbalance! Electrostatics Polarization Polarization is the separation of charge In a conductor, free electrons can move around the surface of the material, leaving one side positive and the other side negative. In

More information

Physics Electricity & Op-cs Lecture 8 Chapter 24 sec Fall 2017 Semester Professor

Physics Electricity & Op-cs Lecture 8 Chapter 24 sec Fall 2017 Semester Professor Physics 24100 Electricity & Op-cs Lecture 8 Chapter 24 sec. 1-2 Fall 2017 Semester Professor Kol@ck How Much Energy? V 1 V 2 Consider two conductors with electric potentials V 1 and V 2 We can always pick

More information

Coulomb s constant k = 9x10 9 N m 2 /C 2

Coulomb s constant k = 9x10 9 N m 2 /C 2 1 Part 2: Electric Potential 2.1: Potential (Voltage) & Potential Energy q 2 Potential Energy of Point Charges Symbol U mks units [Joules = J] q 1 r Two point charges share an electric potential energy

More information

Lesson 3. Electric Potential. Capacitors Current Electricity

Lesson 3. Electric Potential. Capacitors Current Electricity Electric Potential Lesson 3 Potential Differences in a Uniform Electric Field Electric Potential and Potential Energy The Millikan Oil-Drop Experiment Capacitors Current Electricity Ohm s Laws Resistance

More information

Potentials and Fields

Potentials and Fields Potentials and Fields Review: Definition of Potential Potential is defined as potential energy per unit charge. Since change in potential energy is work done, this means V E x dx and E x dv dx etc. The

More information

SPH 4U: Unit 3 - Electric and Magnetic Fields

SPH 4U: Unit 3 - Electric and Magnetic Fields Name: Class: _ Date: _ SPH 4U: Unit 3 - Electric and Magnetic Fields Modified True/False (1 point each) Indicate whether the statement is true or false. If false, change the identified word or phrase to

More information

INDIAN SCHOOL MUSCAT FIRST TERM EXAMINATION PHYSICS

INDIAN SCHOOL MUSCAT FIRST TERM EXAMINATION PHYSICS Roll Number SET NO. General Instructions: INDIAN SCHOOL MUSCAT FIRST TERM EXAMINATION PHYSICS CLASS: XII Sub. Code: 04 Time Allotted: Hrs 0.04.08 Max. Marks: 70. All questions are compulsory. There are

More information

Lecture 13 ELECTRICITY. Electric charge Coulomb s law Electric field and potential Capacitance Electric current

Lecture 13 ELECTRICITY. Electric charge Coulomb s law Electric field and potential Capacitance Electric current Lecture 13 ELECTRICITY Electric charge Coulomb s law Electric field and potential Capacitance Electric current ELECTRICITY Many important uses Historical Light Heat Rail travel Computers Central nervous

More information

PHYSICS. Electrostatics

PHYSICS. Electrostatics Electrostatics Coulomb s Law: SYNOPSIS SI unit of electric intensity is NC -1 Dimensions The electric intensity due to isolated point charge, Electric dipole moment, P = q (2a), SI unit is C m Torque on

More information

2014 F 2014 AI. 1. Why must electrostatic field at the surface of a charged conductor be normal to the surface at every point? Give reason.

2014 F 2014 AI. 1. Why must electrostatic field at the surface of a charged conductor be normal to the surface at every point? Give reason. 2014 F 1. Why must electrostatic field at the surface of a charged conductor be normal to the surface at every point? Give reason. 2. Figure shows the field lines on a positive charge. Is the work done

More information

Chapter 15. Electric Forces and Electric Fields

Chapter 15. Electric Forces and Electric Fields Chapter 15 Electric Forces and Electric Fields First Observations Greeks Observed electric and magnetic phenomena as early as 700 BC Found that amber, when rubbed, became electrified and attracted pieces

More information

7. A capacitor has been charged by a D C source. What are the magnitude of conduction and displacement current, when it is fully charged?

7. A capacitor has been charged by a D C source. What are the magnitude of conduction and displacement current, when it is fully charged? 1. In which Orientation, a dipole placed in uniform electric field is in (a) stable (b) unstable equilibrium. 2. Two point charges having equal charges separated by 1 m in distance experience a force of

More information

Chapter 21. And. Electric Potential due to Point Charges. Capacitors

Chapter 21. And. Electric Potential due to Point Charges. Capacitors Chapter 21 Electric Potential due to Point Charges And Capacitors Potential Difference, commonly called Voltage Recall: E = F/q o = force per unit charge (units: N/C) V = W/q o = work per unit charge

More information

Chapter 29. Electric Potential: Charged Conductor

Chapter 29. Electric Potential: Charged Conductor hapter 29 Electric Potential: harged onductor 1 Electric Potential: harged onductor onsider two points (A and B) on the surface of the charged conductor E is always perpendicular to the displacement ds

More information

Algebra Based Physics Electric Field, Potential Energy and Voltage

Algebra Based Physics Electric Field, Potential Energy and Voltage 1 Algebra Based Physics Electric Field, Potential Energy and Voltage 2016 04 19 www.njctl.org 2 Electric Field, Potential Energy and Voltage Click on the topic to go to that section Electric Field *Electric

More information

You should be able to demonstrate and show your understanding of:

You should be able to demonstrate and show your understanding of: OCR B Physics H557 Module 6: Field and Particle Physics You should be able to demonstrate and show your understanding of: 6.1: Fields (Charge and Field) Field: A potential gradient Field Strength: Indicates

More information

Physics Will Farmer. May 5, Physics 1120 Contents 2

Physics Will Farmer. May 5, Physics 1120 Contents 2 Physics 1120 Will Farmer May 5, 2013 Contents Physics 1120 Contents 2 1 Charges 3 1.1 Terms................................................... 3 1.2 Electric Charge..............................................

More information

melectron= 9.1x10-31 kg e = 1.6x10-19 C MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

melectron= 9.1x10-31 kg e = 1.6x10-19 C MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Exam #1, PHYS 102 Name Chapters 16, 17, & 18 8 February 2006 Constants k=9x109 Nm2/C2 e o =8.85x10-12 F/m mproton=1.673x10-27 kg melectron= 9.1x10-31 kg e = 1.6x10-19 C MULTIPLE CHOICE. Choose the one

More information

Capacitance, Resistance, DC Circuits

Capacitance, Resistance, DC Circuits This test covers capacitance, electrical current, resistance, emf, electrical power, Ohm s Law, Kirchhoff s Rules, and RC Circuits, with some problems requiring a knowledge of basic calculus. Part I. Multiple

More information

A 12-V battery does 1200 J of work transferring charge. How much charge is transferred? A source of 1.0 µc is meters is from a positive test

A 12-V battery does 1200 J of work transferring charge. How much charge is transferred? A source of 1.0 µc is meters is from a positive test 1 A source of 1.0 µc is 0.030 meters is from a positive test charge of 2.0 µc. (a) What is the force on the test charge? (b) What is the potential energy of the test charge? (c) What is the strength of

More information

Electric Potential Energy and Voltage

Electric Potential Energy and Voltage Slide 1 / 105 Electric Potential Energy and Voltage www.njctl.org Slide 2 / 105 How to Use this File Each topic is composed of brief direct instruction There are formative assessment questions after every

More information

Electrical energy & Capacitance

Electrical energy & Capacitance Electrical energy & Capacitance PHY232 Remco Zegers zegers@nscl.msu.edu Room W109 cyclotron building http://www.nscl.msu.edu/~zegers/phy232.html work previously A force is conservative if the work done

More information

Calculus Relationships in AP Physics C: Electricity and Magnetism

Calculus Relationships in AP Physics C: Electricity and Magnetism C: Electricity This chapter focuses on some of the quantitative skills that are important in your C: Mechanics course. These are not all of the skills that you will learn, practice, and apply during the

More information

COLLEGE PHYSICS Chapter 19 ELECTRIC POTENTIAL AND ELECTRIC FIELD

COLLEGE PHYSICS Chapter 19 ELECTRIC POTENTIAL AND ELECTRIC FIELD COLLEGE PHYSICS Chapter 19 ELECTRIC POTENTIAL AND ELECTRIC FIELD Electric Potential Energy and Electric Potential Difference It takes work to move a charge against an electric field. Just as with gravity,

More information

Physics (

Physics ( Exercises Question 2: Two charges 5 0 8 C and 3 0 8 C are located 6 cm apart At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero

More information

Physics 6B. Practice Final Solutions

Physics 6B. Practice Final Solutions Physics 6B Practice Final Solutions . Two speakers placed 4m apart produce sound waves with frequency 45Hz. A listener is standing m in front of the left speaker. Describe the sound that he hears. Assume

More information

F 13. The two forces are shown if Q 2 and Q 3 are connected, their charges are equal. F 12 = F 13 only choice A is possible. Ans: Q2.

F 13. The two forces are shown if Q 2 and Q 3 are connected, their charges are equal. F 12 = F 13 only choice A is possible. Ans: Q2. Q1. Three fixed point charges are arranged as shown in Figure 1, where initially Q 1 = 10 µc, Q = 15 µc, and Q 3 = 5 µc. If charges Q and Q 3 are connected by a very thin conducting wire and then disconnected,

More information

ELECTROSTATIC CBSE BOARD S IMPORTANT QUESTIONS OF 1 MARKS

ELECTROSTATIC CBSE BOARD S IMPORTANT QUESTIONS OF 1 MARKS ELECTROSTATIC CBSE BOARD S IMPORTANT QUESTIONS OF 1 MARKS 1. Name any two basic properties of electric charge. [1] 2. Define the term electric dipole-moment. [1] 3. Write the physical quantity, which has

More information

Class XII Chapter 1 Electric Charges And Fields Physics

Class XII Chapter 1 Electric Charges And Fields Physics Class XII Chapter 1 Electric Charges And Fields Physics Question 1.1: What is the force between two small charged spheres having charges of 2 10 7 C and 3 10 7 C placed 30 cm apart in air? Answer: Repulsive

More information

Physics 2020: Sample Problems for Exam 1

Physics 2020: Sample Problems for Exam 1 Physics 00: Sample Problems for Eam 1 1. Two particles are held fied on the -ais. The first particle has a charge of Q 1 = 6.88 10 5 C and is located at 1 = 4.56 m on the -ais. The second particle has

More information

Practice Exam 1. Necessary Constants and Equations: Electric force (Coulomb s Law): Electric field due to a point charge:

Practice Exam 1. Necessary Constants and Equations: Electric force (Coulomb s Law): Electric field due to a point charge: Practice Exam 1 Necessary Constants and Equations: Electric force (Coulomb s Law): Electric field due to a point charge: Electric potential due to a point charge: Electric potential energy: Capacitor energy:

More information

Chapter 24. Capacitance and Dielectrics Lecture 1. Dr. Armen Kocharian

Chapter 24. Capacitance and Dielectrics Lecture 1. Dr. Armen Kocharian Chapter 24 Capacitance and Dielectrics Lecture 1 Dr. Armen Kocharian Capacitors Capacitors are devices that store electric charge Examples of where capacitors are used include: radio receivers filters

More information

Greeks noticed when they rubbed things against amber an invisible force of attraction occurred.

Greeks noticed when they rubbed things against amber an invisible force of attraction occurred. Ben Franklin, 1750 Kite Experiment link between lightening and sparks Electrostatics electrical fire from the clouds Greeks noticed when they rubbed things against amber an invisible force of attraction

More information

Physics 222, Spring 2010 Quiz 3, Form: A

Physics 222, Spring 2010 Quiz 3, Form: A Physics 222, Spring 2010 Quiz 3, Form: A Name: Date: Instructions You must sketch correct pictures and vectors, you must show all calculations, and you must explain all answers for full credit. Neatness

More information

ISLAMABAD ACADEMY PHYSICS FOR 10TH CLASS (UNIT # 15)

ISLAMABAD ACADEMY PHYSICS FOR 10TH CLASS (UNIT # 15) PHYSICS FOR 10TH CLASS (UNIT # 15) SHORT QUESTIONS Define the term If in the presence of a charged body, an insulated Electrostatic induction? conductor has like charges at one end and unlike charges at

More information

Electrical energy & Capacitance

Electrical energy & Capacitance Electrical energy & Capacitance PHY232 Remco Zegers zegers@nscl.msu.edu Room W109 cyclotron building http://www.nscl.msu.edu/~zegers/phy232.html work previously A force is conservative if the work done

More information

Electrostatics. 3) positive object: lack of electrons negative object: excess of electrons. Particle Mass Electric Charge. m e = 9.

Electrostatics. 3) positive object: lack of electrons negative object: excess of electrons. Particle Mass Electric Charge. m e = 9. Electrostatics 1) electric charge: 2 types of electric charge: positive and negative 2) charging by friction: transfer of electrons from one object to another 3) positive object: lack of electrons negative

More information